David Cameron will on Monday launch a scathing attack on what he calls the "culture of entitlement" in the welfare system, as he warns that claimants with three or more children may start to lose access to benefits, and almost everyone aged under 25 will lose housing benefit.

The prime minister will claim there is now a damaging and divisive gap in Britain between those enjoying privileges inside the welfare system and those resentfully struggling outside. It is likely to be seen on the left as the death-knell for Cameron's brand of compassionate conservatism.

He will also single out lone parents of multiple children as a focus for cuts and insist the welfare system should be a safety net available only to those with no independent means of support. The reforms could see a range of benefits targeted, including income support payments.

The speech represents a shift in the prime minister's political management of the coalition because he will openly acknowledge that some of the proposals cannot be delivered in concert with the Liberal Democrats, and will have to wait for a Conservative majority government after 2015.

He says he hopes the Lib Dems will co-operate on some of the proposals, but "given the scale of change I've suggested, and the long time-frames involved, I am exploring these issues not just as leader of a coalition but as a leader of the Conservative party who is looking ahead to the programme we will set out to the country at the next election".

The Lib Dem Treasury chief secretary, Danny Alexander, gently rebuffed this, saying the focus should be on introducing universal credit in this parliament.

In the single most controversial passage of the speech, Cameron will assert: "We have been encouraging working-age people to have children and not work, when we should be enabling working-age people to work and have children. So it's time we asked some serious questions about the signals we send out through the benefits system."

He will say: "If you are a single parent living outside London, if you have four children and you're renting a house on housing benefit, then you can claim almost £25,000 a year. That is more than the average take-home pay of a farm worker and nursery nurse put together. That is a fundamental difference. And it's not a marginal point.

"There are more than 150,000 people who have been claiming income support for over a year who have three or more children … and 57,000 who have four or more children. The bigger picture is that today, one in six children in Britain is living in a workless household – one of the highest rates in Europe."

Cameron will admit this is difficult territory, but will say that at a time of austerity, "it is right to ask whether those in the welfare system should not be faced with the same kinds of decisions that working people have to wrestle with when they have a child."

Calling for a national debate on welfare, he will insist that compassion should not be measured by the size of a welfare cheque. He will also turn his fire on young people aged under 24 on housing benefit. He will say: "For literally millions, the passage to independence is several years living in their childhood bedroom as they save up to move out; while for many others, it's a trip to the council where they can get housing benefit at 18 or 19 – even if they're not actively seeking work."

Cameron is targeting the current 210,000 people aged 16 to 24 who are social housing tenants, although it is not clear if all of them will be single. He says the measure could save £1bn, but will not apply to victims of domestic violence.

The government has already capped housing benefit for anyone aged under 35 renting from a private landlord, so the maximum is the same as renting a single room in a shared house. The government is forecasting that housing benefit expenditure will peak in 2012/13 at £23.2bn, before falling back to £21.4bn in 2016/17.

Ministers have signalled that they are looking for a further £10bn in welfare cuts, mainly after the next election.

However, Iain Duncan Smith, the work and pensions secretary, appeared to suggest the housing benefit payment system for under-25s would be restricted rather than scrapped altogether.

"The details of these, of course, we have to be careful about," Duncan Smith told the BBC Radio 4 Today programme.

"We have to be sensitive to the different reasons people have housing - people coming out of care, being in difficulties in foster care."

Duncan Smith claimed that the age at which young people move into social housing had dropped to 21 years old and the question Cameron was posing is the degree to which this is caused by families realising that they can get "a child of theirs into social housing if they are no longer living at home".

He said: "He's looking, quite rightly, at the balance between those families that work and try and do the right things against those families that aren't necessarily working and have understood how to work the system."

The work and pension secretary insisted that Cameron "wants to invite the nature of the debate and discussion about what people genuinely think on the back of what we have changed" in this parliament, such as universal credit, benefit reforms and work programmes.

The three questions that needed to be posed now centred on working age benefits, said Duncan Smith: "What is it for? Who should receive it? What the limits of state provision should be - and should there be limits? And what kinds of contributions should we expect from those receiving benefits?"

He went on: "That is why he is talking about this reforms past the next election because by then we will have a much better and stronger feel about where the successes are and where the things are that we need to move on."

Labour's Liam Byrne said the prime minister was taking the "wrong approach".

The shadow work and pensions secretary said that the Labour party didn't disagree with the "basic principle" that work should be encouraged, but argued that the Conservatives' cutting of tax credits was the wrong approach for the long-term.

"We don't disagree with the basic principle that you should be better off in work. That's why Labour introduced tax credits that helped get millions back into work.

"That's why we're angry at the way they're cutting tax credits, which means that thousands of people are actually better off on benefits than in work. I think he's coming at it from the wrong approach for the long term."

In other measures, Cameron may also announce plans to tighten the definition of homelessness, a shift to regionally set benefits, and measures to tighten the requirements to actively seek work before receiving jobseeker's allowance .

For those that have not found work after two years on jobseeker's allowance, he will say they must undertake some form of compulsory community work, such as tidying parks.

As part of a broader argument about a welfare divide in the UK, he will claim: "We have, in some ways, created a welfare gap in this country – between those living long term in the welfare system and those outside it. Those within it grow up with a series of expectations: you can have a home of your own, the state will support you whatever decisions you make, you will always be able to take out no matter what you put in.

"This has sent out some incredibly damaging signals. That it pays not to work. That you are owed something for nothing. It gave us millions of working-age people sitting at home on benefits even before the recession hit. It created a culture of entitlement. And it has led to huge resentment amongst those who pay into the system, because they feel that what they're having to work hard for, others are getting without having to put in the effort."

Cameron will also say his crackdown will apply only to those of working age and not to pensioners. He will say: "Two years ago I made a promise to the elderly of this country and I am keeping it. I was elected on a mandate to protect those benefits – so that is what we have done."